42      The May Department Stores Company

Exhibit 32

Certification Pursuant to Section 906 of The Sarbanes-Oxley Act of 2002
(18 U.S.C. § 1350, As Adopted)

In connection with the Annual Report of The May Department Stores Company (the “Company”) on Form 10-K for the period ending January 29, 2005, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), we, John L. Dunham, Chairman, President, and Chief Executive Officer, and Thomas D. Fingleton, Executive Vice President and Chief Financial Officer of the Company, each certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (18 U.S.C. § 1350, as adopted), that:

1.	The Report fully complies with the requirements of section 13(a) or section 15(d) of the Securities Exchange Act of 1934, and
2.	The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: March 25, 2005

/s/	John L. Dunham	/s/	Thomas D. Fingleton
	John L. Dunham		Thomas D. Fingleton
	Chairman, President and		Executive Vice President and
	Chief Executive Officer		Chief Financial Officer